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COMBINATORIAL DEPLETION · 8D · RANK-9 · 70% DEPTH

8-Deck Nine-Pip Card Depletion at 70% Penetration (5% Audit DEP447)

Removing 26 of 32 Nine-Pip Card (Rank-9) cards at 70% penetration of a 8-deck (416-card) shoe leaves 6 Rank-9 cards inside a 125-card stub (DEP447), producing 45.8588% Banker wins, 44.6257% Player wins, 9.5156% Ties, and a 1.0599% Banker house edge under 5%.

Banker EV (5% Vig)
-1.0599%
Player EV (1:1)
-1.2331%
Rank-9 in 125-Card Stub
6/32
Single-Hand Std Dev
0.9392
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

Open this shoe in /calculator
Big Road B B P P B B P P B B P P B B P B
Big Eye Boy = = = = = = ≠ = = = = = = =
Small Road = = = = = = ≠ ≠ = = = =
Cockroach Pig = = = = = = ≠ ≠ ≠ =

Reference shoe scoreboard (BBPPBBPPBBPPBPTBPB) illustrating derived-road symmetry checks alongside DEP447 (8D Rank-9 at 70% depth).

Big Road B is Banker, P is Player Roads under it Red (=): repeating Blue (≠): breaking
Step-by-Step Mark Proofs (Rule 1 & Rule 2)
Big Eye Boy Mark #2

Column 2 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

  1. Column 3 starts, so use Rule 1: compare Column 2 with Column 1, 1 column further back.
  2. Column 2 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 2, the one that just finished, with Column 1.

Small Road Mark #2

Column 3 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

  1. Column 4 starts, so use Rule 1: compare Column 3 with Column 1, 2 columns further back.
  2. Column 3 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 3, the one that just finished, with Column 1.

Cockroach Pig Mark #2

Column 4 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 1, 3 columns further back.
  2. Column 4 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 1.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP447)
125 / 416 Cards

70% penetration depth in 8D (eight-deck Macau, Las Vegas Strip, and Singapore standard shoes).

Rank-9 Remaining
6 of 32 Cards

26 9-pip cards (top Natural 9 generator) removed from the 8D pack.

Banker EV (5% Vig)
-1.0599%

Resolved at 45.8588% Banker win rate under 5% settlement.

Player EV (1:1)
-1.2331%

Resolved at 44.6257% Player win rate with 0.9392 unit standard deviation.

Tie Incidence (8:1)
9.5156%

Produces a 14.3600% house hold on the 8-to-1 Tie wager in state DEP447.

FINITE-SHOE ENUMERATION · DEP447

How Nine-Pip Card Depletion at 70% Depth Impacts 8D (5% Vig)

Shoe-stub analysis DEP447 inspects 125 remaining cards at 70% penetration of a 416-card (8D) pack after 26 Nine-Pip Card cards have cleared, leaving 6 Rank-9 cards and a 1.0599% 5% Banker edge.

In 8D audit DEP447 (125/416 stub at 70% depth), when 9s are depleted (dep447-rank-9) late in the shoe, more (125c) hands bypass four-card natural resolution (dep447-rank-9·125c) and enter the five- and six-card tableau. Removing 26 Rank-9 cards (-0.23 bps per card) alongside 5% Vig rules sets Tie hold to 14.3600% (9.5156% frequency).

State DEP447 (8D, 70% depth, 6/32 Rank-9 left, 5% Vig)
Wager / MetricState DEP447 Value8D BaselineSettlement Note
DEP447 Banker (5% Vig)45.8588% (-1.0599% EV)45.8597%DEP447 8D 70% (6 Rank-9)
DEP447 Player (1:1)44.6257% (-1.2331% EV)44.6247%DEP447 125-card 8D stub (0.9392 SD)
DEP447 Tie (8:1)9.5156% (-14.3600% EV)9.5156%DEP447 Rank-9 (26 out, 6 in)
TABLEAU & SCOREBOARD SEPARATION · DEP447

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP447 · 8D)

Whether DEP447 is observed in eight-deck Macau, Las Vegas Strip, and Singapore standard shoes at 70% depth (125/416 cards left, 6 Rank-9 remaining), 5% Vig settlement locks Banker EV at -1.0599% and Player EV at -1.2331% with 9.5156% Ties.

  • DEP447 (8D 70%): 125/416 cards with 6/32 Rank-9 (7A).
  • DEP447 (Rank-9 split): 45.8588% Banker, 44.6257% Player, 9.5156% Tie in 125 8D cards (7B).
  • DEP447 (5% Vig EV): -1.0599% Banker, -1.2331% Player, -14.3600% Tie, 0.9392 SD at 70% (7C).
  • DEP447 (8D roads): red/blue marks log Big Road columns, never 6 Rank-9 stub count (7D).
Table Reality Check

Myth vs. Truth

MythWhen 26 Nine-Pip Card cards leave a 8D shoe by 70% depth (DEP447), Big Eye Boy red or blue marks show whether Banker or Player will win next.
TruthDerived-road red and blue marks only compare Big Road column lengths and never track Rank-9 stub counts (6/32 in 125 cards); Banker carries a -1.0599% expectation under 5%.
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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
  • 74 interactive lesson scoreboards and 94 inline quiz checks with plain-English mark feedback
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